**2. Related Work**

The recent research for NTL detection is around hardware or non-hardware solutions. Due to hardware based solution needing further special sensors, the cost and efficiency can hardly satisfy electricity providers even if it has higher accuracy [12]. With the growing of the smart grid and implementation of advanced metering infrastructure (AMI) systems, electricity providers collect and hold various and massive SM data. Hence, non-hardware solutions are more acceptable to electricity providers, especially data oriented methods. Hence, this section only presents a brief survey of the state-of-the-art on data oriented NTL detection methods.

According to implemented machine learning algorithms, data oriented methods could be roughly categorized into three types:


not been demonstrated enough for detecting NTL. However, semi-supervised learning still is competitive and hopeful choice for detecting NTL when it meets deep learning.

Summary, most proposals meet following limitations: (1) Electricity consumption is not enough to classify normal and abnormal cases in all possible scenarios; (2) Artificial NTL samples are different from realistic cases and lose effect on industrial customers; (3) Performance of these methods still needs to be greatly improved.

In the recent years, the field of machine-learning has produced several pivotal advances that address complex problems. Deep learning simulates the brain's structure with multiple layers of neurons, fitting complex functions, and characterizing the input data's distribution, has demonstrated excellent capacity of automatically learning features. It is widely adopted in computer vision [24], speech-recognition [25], natural language processing [26], etc. and has achieved huge success. Simultaneously, a sequence of semi-supervised deep learning models [27–29] have been proposed. It is demonstrated that they had achieved remarkable success in image classification tasks. So, grea<sup>t</sup> potential exists that deep learning would contribute a lot to NTL detection application, the research about which is just in the beginning phase.

The electrical magnitudes are grea<sup>t</sup> different from data which they handled. Firstly, electrical magnitudes are consisting of multiple time series data, such as voltage, current, etc. Secondary, the dimension of electrical magnitudes is significantly different from image and audio. Furthermore, the knowledge has been naturally embedded in the picture or audio, however, electrical magnitudes do not contain any domain knowledge. Therefore, this study attempts to propose a novel semi-supervised deep learning model to overcome the limitations of the above existing works and detect NTL accurately.
